# Weighted Average Cost of Capital

WACC is a very important cost figure for any company (Pratt et al. 2014). It is defined as where:

D = debt (long-term loans, corporate bonds, etc.) (dollars)

E = equity (stocks) (dollars) t = corporate tax rate (percent)

V = E + D (dollars)

Ke = cost of equity capital (e.g., 0.15-0.18)

Kd = cost of debt capital (e.g., 0.08 = yield to maturity [YTM] rate for bonds, plus cost associated with lost growth opportunity)

In general, an increase in leverage (e.g., adding more debts) reduces the firm's WACC. This is due to the tax deductibility of interest payments associated with the debt. For many companies, WACC is typically in the range of 8%-16%.

## Weighted average cost capital formula

All variables in the weighted average cost of capital (WACC) formula refer to the firm as a whole.

Where TC is the corporate tax rate.

Also the WACC formula is:

WACC  =  (E/V x Re)  +  ((D/V x Rd)  x  (1 – T))

E = market value of the firm’s equity
D = market value of the firm’s debt
V = total value of capital (equity plus debt)
E/V = percentage of capital that is equity
D/V = percentage of capital that is debt
Re = cost of equity
Rd = cost of debt (yield to maturity on existing debt)
T = tax rate

The after-tax WACC can be used as the discount rate if

1. The project has the same business risk as the average project of the firm

2. The project is financed with the same amount of debt and equity

If condition 1 is violated the right discount factor is the required rate of return on an equivalently risky investment, whereas if condition 2 is violated the WACC should be adjusted to the right financing mix. This adjustment can be carried out in three steps:

- Step 1: Calculate the opportunity cost of capital

- Calculate the opportunity cost of capital without corporate taxation.

- Step 2: Estimate the cost of debt, rD, and cost of equity, rE, at the new debt level

- Step 3: Recalculate WACC

o "Relever the WACC" by estimating the WACC with the new financing weights

Example:

- Consider a firm with a debt and equity ratio of 40% and 60%, respectively. The required rate of return on debt and equity is 7% and 12.5%, respectively. Assuming a 30% corporate tax rate the after-tax WACC of the firm is:

- The firm is considering investing in a new project with a perpetual stream of cash flows of \$11.83 million per year pre-tax. The project has the same risk as the average project of the firm.

- Given an initial investment of \$125 million, which is financed with 20% debt, what is the value of the project?

- The first insight is that although the business risk is identical, the project is financed with lower financial leverage. Thus, the WACC cannot be used as the discount rate for the project. Rather, the WACC should be adjusted using the three step procedure.

- Step 1: Estimate opportunity cost of capital, i.e. estimate r using a 40% debt ratio, 60% equity ration as well as the firm's cost of debt and equity

- Step 2: Estimate the expected rate of return on equity using the project's debt-equity ratio. As the debt ratio is equal to 20%, the debt-equity ratio equals 25%.

- Step 3: Estimate the project's WACC

- The adjusted WACC of 9.86% can be used as the discount rate for the new project as it reflects the underlying business risk and mix of financing. As the project requires an initial investment of \$125 million and produced a constant cash flow of \$11.83 per year for ever, the projects NPV is:

- In comparison the NPV is equal to \$5.03 if the company WACC is used as the discount rate. In this case we would have invested in a negative NPV project if we ignored that the project was financed with a different mix of debt and equity.

## Examples and analysis of The Weighted Average Cost of Capital (WACC)

Let us begin our analysis by first defining an overall cost of capital in taxless world where management has access to only two sources of finance: equity and debt.

A general formula for WACC is given by the formula for a simple weighted average:

where: K = WACC,

Ke = cost of equity K = cost of debt

VE = market value of equity VD = market value of debt

If we now introduce corporate taxation (at a rate t) the after tax cost of debt Kdt should be substituted into the preceding equation using the appropriate debt formulae from Chapter Six as follows.

This is equivalent to:

Equations (2) and (3) may be rewritten using simpler notation. For example, with tax:

where: WE = the weighting applied to equity (VE / VE + VD) WD = the weighting applied to debt (VD / VE + VD)

Thus, a firm financed equally by equity and debt yielding 10 percent and 5 percent, respectively, would calculate its WACC using Equation (4)as follows:

K = 10% (0.5) + 5% (0.5) = 7.5%

Activity 1

Given the following company data:

K = 12%, Kd = 8%, VE = £6 million, VD = 4 million

Calculate WACC and jot down your thoughts on any assumptions that might validate its use as a discount rate for project appraisal before reading the next section

The individual costs of equity and debt capital are weighted by their proportion of the company's total market value. Using Equation (1) and simplifying:

K = [(0.12 x 0.6) + (0.08 x 0.4)] / 1.0 = 0.104

So, the WACC used as the company discount rate for new project appraisal is 10.4 percent. 7.2 WACC Assumptions

WACC use as a corporate discount rate for investment appraisal depends upon three assumptions.

- New projects have the same risk-return profile as the company's existing activities.

- Each project is marginal to the scale of existing operations.

- The company will retain its existing capital structure, leaving financial risk unchanged.

The reason for the first assumption is obvious. A company's component capital costs reflect the variability of future expected dividend and interest flows. Thus, it follows, that WACC also reflects the overall risk of these combined flows. So, if we use this figure as a discount rate in project appraisal, the new investment's risk-return characteristics must satisfy the company's existing expected dividend and interest payments.

The second assumption is also common sense. When firms consider new investment, the relevant costs refer to the returns that the company must earn on relatively small incremental additions to its total capital base. From an economic viewpoint, they are marginal costs of capital and are only applicable to the appraisal of marginal investments: projects that are small relative to the size of the company.

Finally, the third assumption is necessary because WACC can only provide an appropriate discount rate if new projects are financed in the same proportion as existing assets. This arises for two reasons.

If a company alters its capital structure, the weights applied to the component costs in the WACC calculation would also change, leading to a new discount rate.

A change in the capital mix (gearing) might also affect the investors' perception of the financial risk associated with their investment in the firm. They may then react by buying or selling (as opposed to holding) their securities, thereby affecting the respective yields which determine the WACC.

For example, a new debt issue could increase the uncertainly experienced by the shareholders when they recognize that debt-holders will receive their claim to earnings (interest) before any dividend payment. With increased risk, they sell their holding equity prices may fall because the market requires a higher return as compensation. For the firm, what seems a simple change in the debt-equity ratio is, therefore, a complex decision. Quite apart from revised weightings at new market prices, it must also consider the explicit marginal cost of issuing debt and the implicit cost to the shareholders of their increased financial risk. All three may combine to produce a drastic change in WACC.

Activity 2

Changes in the financial mix (gearing) of a company and the impact of risk on its overall cost of capital and value do not necessarily invalidate the use of WACC as an investment criterion.

Can you think of any reasons for this?

Whilst corporate investment decisions should determine a firm's overall cost of capital, management should avoid the mistake of always associating the explicit marginal costs of new capital issues with a specific project. Often it will be difficult, if not impossible to assign a particular project to a particular source of finance. A company's funds should therefore be viewed collectively. In as much as finance is withdrawn from a pool of funds to invest in new projects, the pool is replenished as fresh capital is raised from outside, or profits are retained. Thus, the cost of capital used for any particular project is not the cost of a specific source of funds, but the overall cost of the company's pool: namely WACC.

In the short run, it is frequently the case that certain funds might also be secured at advantageous rates depending upon prevailing market conditions. This will encourage firms to depart briefly from their long-run capital structure. Under such circumstances, however, WACC still represents an appropriate discount rate for long-term investment, providing the projects exhibit a similar risk-return profile.

Even if funds are raised explicitly from one source to finance an incremental investment, there are sound reasons for using the WACC as a discount rate, particularly if the change in the capital structure represents a short-run deviation from the desired capital mix. First, a rational choice of funds is a financial decision taken not in relation to the investment decision but in relation to the firm's long-term capital structure. Second, there are substantial economies of scale to be gained in terms of reduced issue costs by raising large amounts of capital from one source and then another.